There has been some recent vigorous discussion of the doctrine of the Trinity at Prosblogion (here and here), and it has become a popular topic in contemporary philosophy of religion. It has always seemed to me, however, that the understanding of the Trinity that is usually under discussion in these arguments is rather Sunday-School-ish. There's nothing wrong with Sunday-School-ish interpretations, but they are not an adequate basis for philosophical discussion. If we're going to be using just a Sunday-School-ish interpretation, we might as well admit openly that we're really just toying with some ideas, not seriously discussing the matter. However, given that this is my attitude, I realized that I should take more trouble to articulate what is needed for an adequate discussion than I have as yet done. Rather than formulate the doctrine in the Quicunque Vult way (which was a simplified summary reached after the major issues had seriously been discussed in detail), we should formulate it in terms of four features:
I. Monarchy. For every property in the set of God-befitting properties, the Father has the property.
II. Distinctness. For any subject, if that subject has a God-befitting property, that subject is the Father if and only if it is not the Son and not the Spirit; it is the Son if and only if it is not the Father and not the Spirit; and it is the Spirit if and only if it is not the Father and not the Son.
III. Consubstantiality. For every property in the set of God-befitting properties, if the Father has the property, the Son has the property and the Spirit has the property.
IV. Unity. For every property in the set of God-befitting properties, if subject X has the property and subject Y has the property, the property had by X and the property had by y is identically the same individual property.
This is certainly much closer to the doctrine of the Trinity as actually formulated by the Church Fathers. The Sunday-School-ish version (which is the simplified Quicunque Vult itself simplified) suffers from (1) unnecessary vagueness; (2) oversimplification, through leaving out a lot that was originally considered essential for correctly understanding the doctrine; and (3) trivialization of the actual historical process of articulating the doctrine. Each of the four features identified above played a significant role in the actual articulation of the doctrine, and each is explicitly discussed by many of the Church Fathers at some length. Any serious discussion of the Trinity has to discuss issues that are at least in the ballpark of these. For instance, discussions of whether the doctrine of the Trinity is consistent are really discussions about whether these four features (monarchy, distinctness, consubstantiality, and unity) are consistent, since if they are, the sense of Three-in-One that is orthodox is the sense governed by their consistency.
Even this formulation is only approximate, however. I am not completely satisfied with it for four reasons in particular:
(1) The formulation above gives no indication of the role of negative theology in the doctrine of the Trinity.
(2) One of my major concerns with most discussions of the Trinity in contemporary philosophy of religion is that they ignore the processions almost entirely. But this should seem fishy from the outset, because all the reasons for articulating the doctrine in the first place (which need to be brought into the discussion because they govern the correct interpretation of the articulated doctrine) had to do with the processions. The above formulation is much better, but it only touches on the processions indirectly (via I and II).
(3) The formulation of the principle of monarchy in particular seems incomplete, and I'm not sure I have the principle of unity quite right. (These two issues go together. The phrase "There is but one God," as traditionally understood, sums up the union of these two principles, so if the formulation of one isn't quite adequate, the adequacy of the other's formulation will be hard to evaluate.)
(4) The formulation above gives no indication of the perichoresis (circumincession or circuminsession). This could be brought into the formulation in one of two ways: if the processions were more clearly delineated, it might possibly show itself as a corollary of one or two of the principles; or it could be added as a distinct principle (but I'm not sure quite how to formulate it).
A sample of relevant readings on each of the four features. (Naturally, there is considerable overlapped; I've very roughly categorized things according to the feature they seem to me to shed more light on):
I. Monarchy. Dionysius of Rome Against the Sabellians (from a fragment cited by Athanasius). Photius Encyclical to the Eastern Patriarchs. Aquinas ST 1.33.1.
II. Distinctness. The original Nicene Creed and its Constantinopolitan recension. Hilary of Poitiers On the Trinity. Quicunque Vult. Anselm On the Procession of the Holy Spirit (PDF). Aquinas ST 1.40.
III. Consubstantiality. Athanasius Four Discourses against the Arians. Gregory of Nyssa On the Holy Spirit, against Macedonius. Gregory of Nyssa, Onthe Holy Trinity and the Godhead of the Holy Spirit. Basil On the Holy Spirit. Gregory Nazianzen Theological Orations. Ambrose On the Faith. Ambrose On the Holy Spirit.
IV. Unity. Gregory of Nyssa On Not Three Gods. Augustine On the Trinity. Anselm Letter to John the Monk concerning Roscelin (PDF). Aquinas ST 1.39.
There are, of course, many others; but these are some of the big ones that are easiest to find. In any case, the above characterization of the doctrine by four features is a bit crude and simplistic; but it will do for a first rough draft in a blog post.
I want to say one more thing, somewhat tangential to this topic, on a claim that was made by Dale Tuggy in the second of the posts. Tuggy argues that the Trinity is not found in Scripture. A full discussion of this issue would require examination of one's particular view of Scripture. It is noteworthy, however, that what interested the Church Fathers was Scripture as preached, practiced, and prayed by the Church. This is one reason why, from Athanasius on, they are all so worried about how the doctrine of the Trinity affects baptism (which, of course, is in the name of the Father, the Son, and the Holy Spirit). Indeed, one of the major problems they had with Arianism was that they couldn't make sense of it in the context of baptism; which for them was not merely something they read about on the page, but something the Church had been doing since before it was reaffirmed in Scripture. In general, the argument of the Church Fathers on the Trinity, abstracting from person differences, is this: The whole of Scripture as preached, practiced, and prayed by the Church rationally commits you to something like the the above four features, on pain of serious (salvation-relevant) inconsistency. Athanasius and Basil can't be refuted by pointing to Scripture as text, because they would simply point to Scripture as lived in the worship of the Church. Verbally they are (of course) the same Scripture; but the one is dead letter, the other living spirit. (The Church Fathers, of course, had none of the 'Deism of the Scriptures' so common today, i.e., the view that God gave a fillip and there was inspired revelation, and then He just let it run on its own. This view couldn't be reconciled with their understanding of the experience of Christ and the Spirit in the life of the Church.) Proof-texting consists in merely pointing to the letter, whatever position you are defending. Serious interpretation requires the spirit.